/*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/
// From gsl by zhuo
/* The maximum n such that gsl_sf_fact(n) does not give an overflow. */
#define GSL_SF_FACT_NMAX 170
/* The maximum n such that gsl_sf_doublefact(n) does not give an overflow. */
#define GSL_SF_DOUBLEFACT_NMAX 297
extern struct {
  int n;
  double f;
  long i;
} fact_table_coupling[GSL_SF_FACT_NMAX + 1] = {
    {0, 1.0, 1L},
    {1, 1.0, 1L},
    {2, 2.0, 2L},
    {3, 6.0, 6L},
    {4, 24.0, 24L},
    {5, 120.0, 120L},
    {6, 720.0, 720L},
    {7, 5040.0, 5040L},
    {8, 40320.0, 40320L},

    {9, 362880.0, 362880L},
    {10, 3628800.0, 3628800L},
    {11, 39916800.0, 39916800L},
    {12, 479001600.0, 479001600L},

    {13, 6227020800.0, 0},
    {14, 87178291200.0, 0},
    {15, 1307674368000.0, 0},
    {16, 20922789888000.0, 0},
    {17, 355687428096000.0, 0},
    {18, 6402373705728000.0, 0},
    {19, 121645100408832000.0, 0},
    {20, 2432902008176640000.0, 0},
    {21, 51090942171709440000.0, 0},
    {22, 1124000727777607680000.0, 0},
    {23, 25852016738884976640000.0, 0},
    {24, 620448401733239439360000.0, 0},
    {25, 15511210043330985984000000.0, 0},
    {26, 403291461126605635584000000.0, 0},
    {27, 10888869450418352160768000000.0, 0},
    {28, 304888344611713860501504000000.0, 0},
    {29, 8841761993739701954543616000000.0, 0},
    {30, 265252859812191058636308480000000.0, 0},
    {31, 8222838654177922817725562880000000.0, 0},
    {32, 263130836933693530167218012160000000.0, 0},
    {33, 8683317618811886495518194401280000000.0, 0},
    {34, 2.95232799039604140847618609644e38, 0},
    {35, 1.03331479663861449296666513375e40, 0},
    {36, 3.71993326789901217467999448151e41, 0},
    {37, 1.37637530912263450463159795816e43, 0},
    {38, 5.23022617466601111760007224100e44, 0},
    {39, 2.03978820811974433586402817399e46, 0},
    {40, 8.15915283247897734345611269600e47, 0},
    {41, 3.34525266131638071081700620534e49, 0},
    {42, 1.40500611775287989854314260624e51, 0},
    {43, 6.04152630633738356373551320685e52, 0},
    {44, 2.65827157478844876804362581101e54, 0},
    {45, 1.19622220865480194561963161496e56, 0},
    {46, 5.50262215981208894985030542880e57, 0},
    {47, 2.58623241511168180642964355154e59, 0},
    {48, 1.24139155925360726708622890474e61, 0},
    {49, 6.08281864034267560872252163321e62, 0},
    {50, 3.04140932017133780436126081661e64, 0},
    {51, 1.55111875328738228022424301647e66, 0},
    {52, 8.06581751709438785716606368564e67, 0},
    {53, 4.27488328406002556429801375339e69, 0},
    {54, 2.30843697339241380472092742683e71, 0},
    {55, 1.26964033536582759259651008476e73, 0},
    {56, 7.10998587804863451854045647464e74, 0},
    {57, 4.05269195048772167556806019054e76, 0},
    {58, 2.35056133128287857182947491052e78, 0},
    {59, 1.38683118545689835737939019720e80, 0},
    {60, 8.32098711274139014427634118320e81, 0},
    {61, 5.07580213877224798800856812177e83, 0},
    {62, 3.14699732603879375256531223550e85, 0},
    {63, 1.982608315404440064116146708360e87, 0},
    {64, 1.268869321858841641034333893350e89, 0},
    {65, 8.247650592082470666723170306800e90, 0},
    {66, 5.443449390774430640037292402480e92, 0},
    {67, 3.647111091818868528824985909660e94, 0},
    {68, 2.480035542436830599600990418570e96, 0},
    {69, 1.711224524281413113724683388810e98, 0},
    {70, 1.197857166996989179607278372170e100, 0},
    {71, 8.504785885678623175211676442400e101, 0},
    {72, 6.123445837688608686152407038530e103, 0},
    {73, 4.470115461512684340891257138130e105, 0},
    {74, 3.307885441519386412259530282210e107, 0},
    {75, 2.480914081139539809194647711660e109, 0},
    {76, 1.885494701666050254987932260860e111, 0},
    {77, 1.451830920282858696340707840860e113, 0},
    {78, 1.132428117820629783145752115870e115, 0},
    {79, 8.946182130782975286851441715400e116, 0},
    {80, 7.156945704626380229481153372320e118, 0},
    {81, 5.797126020747367985879734231580e120, 0},
    {82, 4.753643337012841748421382069890e122, 0},
    {83, 3.945523969720658651189747118010e124, 0},
    {84, 3.314240134565353266999387579130e126, 0},
    {85, 2.817104114380550276949479442260e128, 0},
    {86, 2.422709538367273238176552320340e130, 0},
    {87, 2.107757298379527717213600518700e132, 0},
    {88, 1.854826422573984391147968456460e134, 0},
    {89, 1.650795516090846108121691926250e136, 0},
    {90, 1.485715964481761497309522733620e138, 0},
    {91, 1.352001527678402962551665687590e140, 0},
    {92, 1.243841405464130725547532432590e142, 0},
    {93, 1.156772507081641574759205162310e144, 0},
    {94, 1.087366156656743080273652852570e146, 0},
    {95, 1.032997848823905926259970209940e148, 0},
    {96, 9.916779348709496892095714015400e149, 0},
    {97, 9.619275968248211985332842594960e151, 0},
    {98, 9.426890448883247745626185743100e153, 0},
    {99, 9.332621544394415268169923885600e155, 0},
    {100, 9.33262154439441526816992388563e157, 0},
    {101, 9.42594775983835942085162312450e159, 0},
    {102, 9.61446671503512660926865558700e161, 0},
    {103, 9.90290071648618040754671525458e163, 0},
    {104, 1.02990167451456276238485838648e166, 0},
    {105, 1.08139675824029090050410130580e168, 0},
    {106, 1.146280563734708354534347384148e170, 0},
    {107, 1.226520203196137939351751701040e172, 0},
    {108, 1.324641819451828974499891837120e174, 0},
    {109, 1.443859583202493582204882102460e176, 0},
    {110, 1.588245541522742940425370312710e178, 0},
    {111, 1.762952551090244663872161047110e180, 0},
    {112, 1.974506857221074023536820372760e182, 0},
    {113, 2.231192748659813646596607021220e184, 0},
    {114, 2.543559733472187557120132004190e186, 0},
    {115, 2.925093693493015690688151804820e188, 0},
    {116, 3.393108684451898201198256093590e190, 0},
    {117, 3.96993716080872089540195962950e192, 0},
    {118, 4.68452584975429065657431236281e194, 0},
    {119, 5.57458576120760588132343171174e196, 0},
    {120, 6.68950291344912705758811805409e198, 0},
    {121, 8.09429852527344373968162284545e200, 0},
    {122, 9.87504420083360136241157987140e202, 0},
    {123, 1.21463043670253296757662432419e205, 0},
    {124, 1.50614174151114087979501416199e207, 0},
    {125, 1.88267717688892609974376770249e209, 0},
    {126, 2.37217324288004688567714730514e211, 0},
    {127, 3.01266001845765954480997707753e213, 0},
    {128, 3.85620482362580421735677065923e215, 0},
    {129, 4.97450422247728744039023415041e217, 0},
    {130, 6.46685548922047367250730439554e219, 0},
    {131, 8.47158069087882051098456875820e221, 0},
    {132, 1.11824865119600430744996307608e224, 0},
    {133, 1.48727070609068572890845089118e226, 0},
    {134, 1.99294274616151887673732419418e228, 0},
    {135, 2.69047270731805048359538766215e230, 0},
    {136, 3.65904288195254865768972722052e232, 0},
    {137, 5.01288874827499166103492629211e234, 0},
    {138, 6.91778647261948849222819828311e236, 0},
    {139, 9.61572319694108900419719561353e238, 0},
    {140, 1.34620124757175246058760738589e241, 0},
    {141, 1.89814375907617096942852641411e243, 0},
    {142, 2.69536413788816277658850750804e245, 0},
    {143, 3.85437071718007277052156573649e247, 0},
    {144, 5.55029383273930478955105466055e249, 0},
    {145, 8.04792605747199194484902925780e251, 0},
    {146, 1.17499720439091082394795827164e254, 0},
    {147, 1.72724589045463891120349865931e256, 0},
    {148, 2.55632391787286558858117801578e258, 0},
    {149, 3.80892263763056972698595524351e260, 0},
    {150, 5.71338395644585459047893286526e262, 0},
    {151, 8.62720977423324043162318862650e264, 0},
    {152, 1.31133588568345254560672467123e267, 0},
    {153, 2.00634390509568239477828874699e269, 0},
    {154, 3.08976961384735088795856467036e271, 0},
    {155, 4.78914290146339387633577523906e273, 0},
    {156, 7.47106292628289444708380937294e275, 0},
    {157, 1.17295687942641442819215807155e278, 0},
    {158, 1.85327186949373479654360975305e280, 0},
    {159, 2.94670227249503832650433950735e282, 0},
    {160, 4.71472363599206132240694321176e284, 0},
    {161, 7.59070505394721872907517857094e286, 0},
    {162, 1.22969421873944943411017892849e289, 0},
    {163, 2.00440157654530257759959165344e291, 0},
    {164, 3.28721858553429622726333031164e293, 0},
    {165, 5.42391066613158877498449501421e295, 0},
    {166, 9.00369170577843736647426172359e297, 0},
    {167, 1.50361651486499904020120170784e300, 0},
    {168, 2.52607574497319838753801886917e302, 0},
    {169, 4.26906800900470527493925188890e304, 0},
    {170, 7.25741561530799896739672821113e306, 0},
};

extern struct {
  int n;
  double f;
  long i;
} doub_fact_table_coupling[GSL_SF_DOUBLEFACT_NMAX + 1] = {
    {0, 1.000000000000000000000000000, 1L},
    {1, 1.000000000000000000000000000, 1L},
    {2, 2.000000000000000000000000000, 2L},
    {3, 3.000000000000000000000000000, 3L},
    {4, 8.000000000000000000000000000, 8L},
    {5, 15.00000000000000000000000000, 15L},
    {6, 48.00000000000000000000000000, 48L},
    {7, 105.0000000000000000000000000, 105L},
    {8, 384.0000000000000000000000000, 384L},
    {9, 945.0000000000000000000000000, 945L},
    {10, 3840.000000000000000000000000, 3840L},
    {11, 10395.00000000000000000000000, 10395L},
    {12, 46080.00000000000000000000000, 46080L},
    {13, 135135.0000000000000000000000, 135135L},
    {14, 645120.00000000000000000000000, 645120L},
    {15, 2.02702500000000000000000000000e6, 2027025L},
    {16, 1.03219200000000000000000000000e7, 10321920L},
    {17, 3.4459425000000000000000000000e7, 34459425L},
    {18, 1.85794560000000000000000000000e8, 185794560L},
    {19, 6.5472907500000000000000000000e8, 0},
    {20, 3.7158912000000000000000000000e9, 0},
    {21, 1.37493105750000000000000000000e10, 0},
    {22, 8.1749606400000000000000000000e10, 0},
    {23, 3.1623414322500000000000000000e11, 0},
    {24, 1.96199055360000000000000000000e12, 0},
    {25, 7.9058535806250000000000000000e12, 0},
    {26, 5.1011754393600000000000000000e13, 0},
    {27, 2.13458046676875000000000000000e14, 0},
    {28, 1.42832912302080000000000000000e15, 0},
    {29, 6.1902833536293750000000000000e15, 0},
    {30, 4.2849873690624000000000000000e16, 0},
    {31, 1.91898783962510625000000000000e17, 0},
    {32, 1.37119595809996800000000000000e18, 0},
    {33, 6.3326598707628506250000000000e18, 0},
    {34, 4.6620662575398912000000000000e19, 0},
    {35, 2.21643095476699771875000000000e20, 0},
    {36, 1.67834385271436083200000000000e21, 0},
    {37, 8.2007945326378915593750000000e21, 0},
    {38, 6.3777066403145711616000000000e22, 0},
    {39, 3.1983098677287777081562500000e23, 0},
    {40, 2.55108265612582846464000000000e24, 0},
    {41, 1.31130704576879886034406250000e25, 0},
    {42, 1.07145471557284795514880000000e26, 0},
    {43, 5.6386202968058350994794687500e26, 0},
    {44, 4.7144007485205310026547200000e27, 0},
    {45, 2.53737913356262579476576093750e28, 0},
    {46, 2.16862434431944426122117120000e29, 0},
    {47, 1.19256819277443412353990764062e30, 0},
    {48, 1.04093968527333324538616217600e31, 0},
    {49, 5.8435841445947272053455474391e31, 0},
    {50, 5.2046984263666662269308108800e32, 0},
    {51, 2.98022791374331087472622919392e33, 0},
    {52, 2.70644318171066643800402165760e34, 0},
    {53, 1.57952079428395476360490147278e35, 0},
    {54, 1.46147931812375987652217169510e36, 0},
    {55, 8.6873643685617511998269581003e36, 0},
    {56, 8.1842841814930553085241614926e37, 0},
    {57, 4.9517976900801981839013661172e38, 0},
    {58, 4.7468848252659720789440136657e39, 0},
    {59, 2.92156063714731692850180600912e40, 0},
    {60, 2.84813089515958324736640819942e41, 0},
    {61, 1.78215198865986332638610166557e42, 0},
    {62, 1.76584115499894161336717308364e43, 0},
    {63, 1.12275575285571389562324404931e44, 0},
    {64, 1.13013833919932263255499077353e45, 0},
    {65, 7.2979123935621403215510863205e45, 0},
    {66, 7.4589130387155293748629391053e46, 0},
    {67, 4.8896013036866340154392278347e47, 0},
    {68, 5.0720608663265599749067985916e48, 0},
    {69, 3.3738248995437774706530672060e49, 0},
    {70, 3.5504426064285919824347590141e50, 0},
    {71, 2.39541567867608200416367771623e51, 0},
    {72, 2.55631867662858622735302649017e52, 0},
    {73, 1.74865344543353986303948473285e53, 0},
    {74, 1.89167582070515380824123960272e54, 0},
    {75, 1.31149008407515489727961354964e55, 0},
    {76, 1.43767362373591689426334209807e56, 0},
    {77, 1.00984736473786927090530243322e57, 0},
    {78, 1.12138542651401517752540683649e58, 0},
    {79, 7.9777941814291672401518892225e58, 0},
    {80, 8.9710834121121214202032546920e59, 0},
    {81, 6.4620132869576254645230302702e60, 0},
    {82, 7.3562883979319395645666688474e61, 0},
    {83, 5.3634710281748291355541151243e62, 0},
    {84, 6.1792822542628292342360018318e63, 0},
    {85, 4.5589503739486047652209978556e64, 0},
    {86, 5.3141827386660331414429615754e65, 0},
    {87, 3.9662868253352861457422681344e66, 0},
    {88, 4.6764808100261091644698061863e67, 0},
    {89, 3.5299952745484046697106186396e68, 0},
    {90, 4.2088327290234982480228255677e69, 0},
    {91, 3.2122956998390482494366629620e70, 0},
    {92, 3.8721261107016183881809995223e71, 0},
    {93, 2.98743500085031487197609655470e72, 0},
    {94, 3.6397985440595212848901395509e73, 0},
    {95, 2.83806325080779912837729172696e74, 0},
    {96, 3.4942066022971404334945339689e75, 0},
    {97, 2.75292135328356515452597297515e76, 0},
    {98, 3.4243224702511976248246432895e77, 0},
    {99, 2.72539213975072950298071324540e78, 0},
    {100, 3.4243224702511976248246432895e79, 0},
    {101, 2.75264606114823679801052037785e80, 0},
    {102, 3.4928089196562215773211361553e81, 0},
    {103, 2.83522544298268390195083598919e82, 0},
    {104, 3.6325212764424704404139816015e83, 0},
    {105, 2.97698671513181809704837778865e84, 0},
    {106, 3.8504725530290186668388204976e85, 0},
    {107, 3.1853757851910453638417642339e86, 0},
    {108, 4.1585103572713401601859261374e87, 0},
    {109, 3.4720596058582394465875230149e88, 0},
    {110, 4.5743613929984741762045187512e89, 0},
    {111, 3.8539861625026457857121505465e90, 0},
    {112, 5.1232847601582910773490610013e91, 0},
    {113, 4.3550043636279897378547301176e92, 0},
    {114, 5.8405446265804518281779295415e93, 0},
    {115, 5.0082550181721881985329396352e94, 0},
    {116, 6.7750317668333241206863982681e95, 0},
    {117, 5.8596583712614601922835393732e96, 0},
    {118, 7.9945374848633224624099499564e97, 0},
    {119, 6.9729934618011376288174118541e98, 0},
    {120, 9.5934449818359869548919399477e99, 0},
    {121, 8.4373220887793765308690683435e100, 0},
    {122, 1.17040028778399040849681667362e102, 0},
    {123, 1.03779061691986331329689540625e103, 0},
    {124, 1.45129635685214810653605267528e104, 0},
    {125, 1.29723827114982914162111925781e105, 0},
    {126, 1.82863340963370661423542637086e106, 0},
    {127, 1.64749260436028300985882145742e107, 0},
    {128, 2.34065076433114446622134575470e108, 0},
    {129, 2.12526545962476508271787968008e109, 0},
    {130, 3.04284599363048780608774948111e110, 0},
    {131, 2.78409775210844225836042238090e111, 0},
    {132, 4.0165567115922439040358293151e112, 0},
    {133, 3.7028500103042282036193617666e113, 0},
    {134, 5.3821859935336068314080112822e114, 0},
    {135, 4.9988475139107080748861383849e115, 0},
    {136, 7.3197729512057052907148953438e116, 0},
    {137, 6.8484210940576700625940095873e117, 0},
    {138, 1.01012866726638733011865555744e119, 0},
    {139, 9.5193053207401613870056733264e119, 0},
    {140, 1.41418013417294226216611778042e121, 0},
    {141, 1.34222205022436275556779993902e122, 0},
    {142, 2.00813579052557801227588724819e123, 0},
    {143, 1.91937753182083874046195391280e124, 0},
    {144, 2.89171553835683233767727763739e125, 0},
    {145, 2.78309742114021617366983317355e126, 0},
    {146, 4.2219046860009752130088253506e127, 0},
    {147, 4.0911532090761177752946547651e128, 0},
    {148, 6.2484189352814433152530615189e129, 0},
    {149, 6.0958182815234154851890356000e130, 0},
    {150, 9.3726284029221649728795922783e131, 0},
    {151, 9.2046856051003573826354437561e132, 0},
    {152, 1.42463951724416907587769802630e134, 0},
    {153, 1.40831689758035467954322289468e135, 0},
    {154, 2.19394485655602037685165496051e136, 0},
    {155, 2.18289119124954975329199548675e137, 0},
    {156, 3.4225539762273917878885817384e138, 0},
    {157, 3.4271391702617931126684329142e139, 0},
    {158, 5.4076352824392790248639591467e140, 0},
    {159, 5.4491512807162510491428083336e141, 0},
    {160, 8.6522164519028464397823346347e142, 0},
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